1. Field of the Invention
The present invention relates to apparatus and methods using Modulated Differential Scanning Calorimetry ("MDSC") to measure the thermal conductivity of materials.
2. Background of the Invention
Thermal conductivity characterizes the ability of a material to conduct heat. Traditional methods for measuring the thermal conductivity of materials comprise imposing a temperature gradient upon a material of known geometry, and measuring the heat flow through the material. The heat flow is measured by, for example, measuring the temperature drop across a sheet of known thermal conductivity.
P. G. Knibbe, J. Phys. E: Sci. Instrum., vol. 20, pp. 1205-1211 (1987) describes a "hot wire" technique for measuring the thermal conductivity of a material. This technique uses a temperature-sensitive resistor wire embedded in a sample of the material. The resistor wire serves the dual function of supplying heat to the specimen, and measuring the temperature change at the wire. This rate of change is related to the thermal conductivity of the sample of the material.
D. G. Cahill and R. O. Pohl, Phys. Rev. B. vol. 35, p. 4067 (1987), and D. G. Cahill, Rev. Sci. Instrum. vol. 61(2), pp. 802-808 (1990), describe a "3.omega." technique for measuring thermal conductivity. This technique uses a temperature sensitive resistive metal film evaporated as a narrow line onto the surface of the sample to simultaneously heat the sample and detect the flow of heat away from the metal line. A current at angular frequency .omega. heats the metal line at a frequency of 2.omega.. Because the resistance of a metal increases with increasing temperature, and this temperature is modulated by the sample thermal conductivity, this produces a small oscillation in the resistance of the metal line, resulting in a voltage across the resistor at a frequency of 3.omega.. The thermal conductivity of the sample is then calculated from the amplitude of the 3.omega. voltage oscillations.
J. H. Flynn and D. M. Levin, Thermochimica Acta, vol. 126, pp. 93-100 (1988), describes a thermal conductivity measurement method, suitable for measuring the thermal conductivity of sheet materials, based upon first-order transitions in a sensor material. A film of the sensor material is placed on a surface of the sheet material. The thermal conductivity measurement is made at the temperature at which the sensor material undergoes a first order transition. For example, if indium is used as the sensor material, the measurement is made at the melting point of indium, i.e., at the temperature at which indium undergoes a first order transition. The flow of heat into the sensor material must match the transition enthalpy. The thermal conductivity of the sheet material is obtained by comparing the data obtained with only the sensor material in the heater of a differential scanning calorimeter, to the data obtained with the sensor material on top of the sheet material in the differential scanning calorimeter.
These techniques are all subject to significant limitations. For example, the hot wire technique requires large samples, long times for the sample to come into equilibrium, and an additional long measurement period. The 3.omega. technique requires a thin metal film in intimate contact with the sample, with fine electrical contacts to the film. The metal film must be thermally isolated from any heat sink, except for the sample being measured. The combination of film and sample is not mechanically robust, and is not readily separable so that other samples can be measured. The first order transition technique is restricted to the temperatures where materials are available with sharp first order transitions.
On the other hand, the present invention provides for quick measurements using small samples. The samples can be easily and rapidly changed. Furthermore, the measurement is not restricted to a set of discrete temperatures.